-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 7, -14, 5, 4, -5, -2, 11, -10, 7, -2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 53697370966801, 'disc_rad': 2707, 'disc_sign': 1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[10, 1], [2, 1]]], [7, [[5, 2], [1, 2]]], [11, [[10, 1], [2, 1]]], [13, [[2, 6]]], [17, [[3, 4]]], [19, [[6, 2]]], [23, [[10, 1], [2, 1]]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[10, 1], [2, 1]]], [41, [[3, 4]]], [43, [[2, 4], [1, 4]]], [47, [[2, 4], [1, 4]]], [53, [[3, 4]]], [59, [[5, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60], 'galois_label': '12T76', 'galt': 76, 'grd': 52.028838157314254, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.4.53697370966801.1', 'local_algs': ['m2707.1.1.0', 'm2707.1.1.0', 'm2707.1.1.0', 'm2707.1.1.0', 'm2707.2.1.1', 'm2707.2.1.1', 'm2707.2.1.1', 'm2707.2.1.1'], 'minimal_sibling': [697, 1349, 695, 7, 12, -6, 6, -2, -1, -2, 1], 'monogenic': 0, 'num_ram': 1, 'r2': 4, 'ramps': [2707], 'rd': 13.936789865083114, 'regulator': {'__RealLiteral__': 0, 'data': '138.27818534649447', 'prec': 60}, 'subfield_mults': [1], 'subfields': ['-1.3.3.-5.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( -\\frac{2086}{949} a^{11} + \\frac{4064}{949} a^{10} + \\frac{398}{73} a^{9} - \\frac{14719}{949} a^{8} + \\frac{17634}{949} a^{7} - \\frac{20004}{949} a^{6} - \\frac{818}{949} a^{5} + \\frac{12060}{949} a^{4} - \\frac{5010}{949} a^{3} - \\frac{11612}{949} a^{2} + \\frac{29358}{949} a - \\frac{7146}{949} \\)', '\\( -\\frac{5060}{949} a^{11} + \\frac{8142}{949} a^{10} + \\frac{1014}{73} a^{9} - \\frac{30129}{949} a^{8} + \\frac{39107}{949} a^{7} - \\frac{40968}{949} a^{6} - \\frac{4894}{949} a^{5} + \\frac{22852}{949} a^{4} - \\frac{11514}{949} a^{3} - \\frac{29128}{949} a^{2} + \\frac{59074}{949} a - \\frac{14467}{949} \\)', '\\( -\\frac{5060}{949} a^{11} + \\frac{8142}{949} a^{10} + \\frac{1014}{73} a^{9} - \\frac{30129}{949} a^{8} + \\frac{39107}{949} a^{7} - \\frac{40968}{949} a^{6} - \\frac{4894}{949} a^{5} + \\frac{22852}{949} a^{4} - \\frac{11514}{949} a^{3} - \\frac{29128}{949} a^{2} + \\frac{59074}{949} a - \\frac{13518}{949} \\)', '\\( \\frac{4905}{949} a^{11} - \\frac{8022}{949} a^{10} - \\frac{960}{73} a^{9} + \\frac{29629}{949} a^{8} - \\frac{38874}{949} a^{7} + \\frac{40467}{949} a^{6} + \\frac{2998}{949} a^{5} - \\frac{22197}{949} a^{4} + \\frac{12401}{949} a^{3} + \\frac{28277}{949} a^{2} - \\frac{58039}{949} a + \\frac{15814}{949} \\)', '\\( -\\frac{2025}{949} a^{11} + \\frac{3129}{949} a^{10} + \\frac{397}{73} a^{9} - \\frac{11614}{949} a^{8} + \\frac{15779}{949} a^{7} - \\frac{16219}{949} a^{6} - \\frac{1229}{949} a^{5} + \\frac{8894}{949} a^{4} - \\frac{4606}{949} a^{3} - \\frac{11822}{949} a^{2} + \\frac{23073}{949} a - \\frac{6372}{949} \\)', '\\( \\frac{2025}{949} a^{11} - \\frac{3129}{949} a^{10} - \\frac{397}{73} a^{9} + \\frac{11614}{949} a^{8} - \\frac{15779}{949} a^{7} + \\frac{16219}{949} a^{6} + \\frac{1229}{949} a^{5} - \\frac{8894}{949} a^{4} + \\frac{4606}{949} a^{3} + \\frac{11822}{949} a^{2} - \\frac{22124}{949} a + \\frac{6372}{949} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/949*a^11 - 62/949*a^10 - 6/73*a^9 - 58/949*a^8 - 326/949*a^7 - 358/949*a^6 - 349/949*a^5 + 57/949*a^4 + 380/949*a^3 - 19/949*a^2 + 177/949*a - 174/949']}
Number field data - 12.4.53697370966801.1